Communication in bounded depth circuits

Abstract

We show that rigidity of matrices can be used to prove lower bounds on depth 2 circuits and communication graphs. We prove a general nonlinear bound on a certain type of circuits and thus, in particular, we determine the asymptotic size of depthd superconcentrators for all depths ≥4 (for even depths ≥4 it has been determined before).

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References

  1. [1]

    N. Alon, andP. Pudlák: Superconcentrators of depth 2 and 3,Journ. of Computer and System Science 48(1) (1994), 194–202.

    Google Scholar 

  2. [2]

    D. Dolev, C. Dwork, N. Pippenger andA. Wigderson: Superconcentrators, generalizers and generalized connectors (preliminary version),Proc. ACM STOC (1983), 42–51.

  3. [3]

    N. Pippenger: Superconcentrators of depth 2,J. Comput. System Sci. 24 (1982), 82–90.

    Google Scholar 

  4. [4]

    N. Pippenger: Communications networks, inHandbook of Theoretical Computer Science, Ed. J. van Leeuwen, Elsevier, (1990), 806–833.

  5. [5]

    N. Pippenger andA. C.-C. Yao: Rearrangeable networks with limited depth,SIAM J. Alg. Disc. Meth. 3 (1981), 411–417.

    Google Scholar 

  6. [6]

    P. Pudlák andP. Savický: On shifting networks,Theoretical Computer Science 116 (1993), 415–419.

    Google Scholar 

  7. [7]

    P. Pudlák andZ. Vavřín: Computation of rigidity of ordern 2/r for one simple matrix,Comment. Math. Univ. Carolinae 32(2) (1991), 213–218.

    Google Scholar 

  8. [8]

    A. A. Razborov: On rigid matrices (in Russian), unpublished.

  9. [9]

    V. Shoup andR. Smolensky: Lower bounds for polynomial evaluation and interpolation,Proc. IEEE FOCS (1991), 378–383.

  10. [10]

    L. G. Valiant: Graph-theoretic arguments in low level complexity,Proc. MFCS 1977, Springer-Verlag LNCS, (1977), 162–176.

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Pudlák, P. Communication in bounded depth circuits. Combinatorica 14, 203–216 (1994). https://doi.org/10.1007/BF01215351

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AMS subject classification code (1991)

  • 68 R 10
  • 05 C 35